Make an appointment with your piano tuner. The best mic set-up in the world won't make an out-of-tune piano sound good. It's also a good idea to have your piano tuner check the functionality of the piano so you can address any issues that may affect the results of your piano recordings. Keys that tend to stick, or stiff and overly noisy pedals can spoil an otherwise perfect piano take, so taking this step can save you from anguish down the road.
Use a stereo pair of quality medium diaphragm condenser mics is the best way to go, since the piano has a very wide frequency range. If your budget is limited, there are still many affordable options on the market that will do a fine job (see Resources), but be sure to buy a matching pair. This way, the mics will have the same response pattern, which should help you avoid out-of-phase issues that may result from using mismatched mics.
Attach your condenser mics to boom-style mic stands. Lift the lid of your piano and set the mics up so that they're both just inside the piano, with one pointing towards the low strings and the other towards the high strings. You'll have to experiment with how far inside the piano to move the mics to get a sound you like. The closer you get the mics to the hammers and strings the more attack you'll get, while moving them further away will result in a more muted tone.
Try recording the room. Have someone play the piano as you walk around the room. Listen for the sweet spot and set up another condenser mic to capture the sound of the piano in the room. This may or may not give you the exact sound you're looking for by itself, but may well give you more options when you combine this sound with the direct mic pair.
Once your piano track is recorded, pan one mic signal to the left and the other to the right for stereo playback. Listen to the sound and gradually bring in the live room mic signal. Experiment with the panning and see if it improves the overall sound of the piano track. Although the piano generally sounds better in stereo, if your mix contains a lot of other instruments and voices, it may pay to pan the piano tracks together for a mono mix and play with the EQ and panning of this track so that it cuts through the mix better.